i think principia mathematica defines 2 first as a certain set size which you have to more or less accept is the 2 we're familiar with. (correct me if i'm wrong there?) the advantage being that it allows for a definition of 2 prior to the definition of addition

...of course, prior to the definition of addition it's not like "1+1" means a damn thing (not that they claim it does, of course)

I never really bothered to fully figure out that book's notation, but I think that's what it says, yeah.

I really shouldn't knock Principia Mathematica. It's a good work for the time it was made, although we have a much better understanding of most of the topics it addresses nowadays (and I have reason to believe Bertrand Russell was a clever and admirable man), I just don't think it's applicable to the question at hand--partly because I think arithmetical addition is well(and simply) defined, but especially since people generally aren't thinking, "2 is identical with the set of all α such that α has some element x, which, when removed from α, leaves a 1-element set" (Principia-Mathematica-to-English-translation stolen from this blog) when they say 1+1=2, and 1+1=2 really wasn't the focus of the book, either._________________butts

Last edited by Heretical Rants on Sat Sep 15, 2012 12:08 am; edited 1 time in total

I really do want to participate in this discussion because its relative to my interests on how people come to "knowledge" but I guess I have to answer this stupid thing first, or else it simply would be uncouth of me to say anything.

Sojobo wrote:

Lich Mong wrote:

Read you're own statements, please.
You did use the in-out numbers in the other fields to claim there was a large disparity in the Engineering in-out numbers.

Of course I use the numbers in the other fields. That's exactly what I've said I'm doing. Why would you pretend to correct me by saying exactly the same things I am saying?

Lich Mong wrote:

That's what I'm objecting to.

Which I think makes no sense, and which you haven't backed up with any reasoning.

Yes, I did. You would have to show that comparing the in numbers to the out numbers across fields were comparable before you could compare them as you did. Each field could(and likely does) have drastically different drop out rates, so the in and out numbers for each has a different variation, since they change at different rates.

I told you that, but you shifted the goal post and started talking about Ember778's original claim(which you misrepresented, but that's neither here nor there because it was not what we were talking about). I was not talking about Ember778's claim, and you know that which makes the whole thing even more upsetting.

If more Engineers drop out than other fields then the change in gender for Engineers would be expected to be more drastic, even if the gender of the people dropping out was perfectly random.(however, it might be unfair for me to expect you to know that. I'd use numbers to help try and illustrate it to you, but I am afraid you'd start twisting them as you did with my other numerical examples, see below)

Sojobo wrote:

Lich Mong wrote:

We are not talking about inferences made about "wild jumps" but the differences of 1% point.

And if you'd at any point mentioned differences of 1% instead of talking about 99% or 50% splits, you would have some momentum for making this point. You didn't.

Anyway, you are still wrong, because 1% changes wouldn't be big enough, as the numbers would still be starkly different. You need for it to have increased 5% per year, each year, to merely "break even" with the other categories, which would still disagree with the original claim that women are bad at engineering, so you'd still be wrong.

I would hope you would understand that I was using larger numbers inorder to illustrate more clearly why your inferences based on a 1% change was not justified.
But, it seems in an attempt to "prove me wrong," you decided to latch on to my hypothetical numbers as if they some how represented my argument. They don't. I was saying "what if 2010 was a slow year for female admissions" but used numbers hoping it would make it more clear in context.

The very fact I have to explain this in such detail NOW shows you either are very stupid (something I find unlikely) or you're trying to misrepresent me to "save face" or whatever. I'd get on a higher horse about such tactics but I used to employ them myself so morally I can't. But,--with that said--please don't think I don't know what you're doing.

Sojobo wrote:

Lich Mong wrote:

So, those are both not what you said you said, and much stronger statements than you said you said.

Those were both exactly what I said I said, and I highlighted my words within your quotations. You copy-pasted the very words you are saying I didn't say. You are wrong.

I'm not even sure how to address this because it relates back to a statement you already admitted was wrong.
So, I guess I won't.

Sojobo wrote:

Lich Mong wrote:

Well, why not your house that it was over 23.2%
That's the number --after all-- it would have to be under for your statements to be reasonable.

And again you are wrong. The number could be 23.5%, or 24%, or 25%, and my statements would all still be perfectly reasonable. I think perhaps you haven't actually looked at the numbers themselves and noticed that the discrepancy is actually quite large and unmistakable.

I think you need to look up the definition of "under." Or you don't realize I was referring to the intake numbers, not the outtake ones. If you read the flow of the conversation it should be clear I was, but I suspect you had blinders on at this point and were going after each of my statements individually instead of in context.

Sojobo wrote:

Lich Mong wrote:

You can't... you can't see how sampling size would... you... y....

As this seems to be the most important issue to you, I'll go ahead and give it several sentences.

First, you said "100%" exactly. This is not referring to sampling size, but rather using a sample at all versus using complete data directly. Your gasps that I don't care about sampling size are quite misplaced.

I repeat, with more clarity, that it is irrelevant whether they used 100% of the data or merely a representative sample. The numbers would have the same meaning and same usefulness for my comments either way.

Second, this is an utterly different argument than anything else you've brought up before. In questioning sample size, you are questioning the validity of the numbers themselves. Obviously, if they have polled too few people, that would render my conclusion unsound. But this still wouldn't have any bearing whatsoever on whether my use of the numbers is valid, which it is.

Third, I don't think this was a poll, and am mystified why you think it might be. You cited the "Council of Graduate Schools". I think the obvious guess is that you have presented actual data gleaned from school records. Your bet that they didn't use "100%" of the data was probably a pretty bad one.

It was a "big deal" because it was a very very stupid thing to say. In fact, it(and this bit) illustrates to me just how little you understand statistics and polls. I thought when you referred to my standard deviation link as "condescending" it meant you had at least a rudimentary understanding of the subject. However, when you started talking about how you assumed the numbers might came from every school everywhere and that you could not see how it would matter as long as the numbers were "representative" it became clear to me just how little you know. You clicking that 'condescending' link might have prevented this whole stupid argument. Now, this is not to call YOU stupid or something, but is to say I don't feel it would be instructive for either of us for me to have to fight through your strawmen and shifting goal posts if you do not even really understand the subject anyway.
Honestly, I still don't. The entire conversation was about error in the statistics, but if you neither think there is any error, because all schools everywhere were polled, or don't grasp the process that goes into numbers like those, AND feel this is a "who's wrong/right how can I showoff" discussion, I don't feel like having it with you.
Again, I do wish I could get on a higher horse about your tactics, but since I did the same thing for a number of years I don't think it would be reasonable. Anyway, make your response, and try to make me look as foolish as you can. Your knowledge of statistics not withstanding, you seem like a clever man so I am sure you'll be able to do just that. I'll not respond (hopefully, if I pass my willsave this time).

Regardless, I am sure you are probably right about the dropout rates anyway, and for all we know they gave those polls out to the sig figs they did because they are good to .1% anyway(but that's unlikely). So, chalk it up as a "win" if you want.

Now, I want to talk about the other stuff, which I've studied less formally and--therefor--find more worthwhile for internet debates.

Ember778, no one will be able to persent you with the proof you ask for because it does not exist. There is no rock solid way of getting that kind of information. But, YOUR belief is not based on anything rock solid either. As has been already labored on, your appeal to "common knowledge" is a known fallacy.

However, I don't think you were trying to say that. I believe what you were trying to say is that "extraordinary claims require extraordinary proof." Which is true, it takes work to overthrow presence. Since we don't have any rock solid ways of getting knowledge we have to use the scientific method to test and retest hypothesis. However, that's what Dogen's evidence IS. Those are papers that use the scientific method to SHOW what he is trying to show. HE is the one with the evidence here, not you. HE is the one with the empirical "proof."

Now, look, maybe his stuff will turn out wrong. Happens, new knowledge comes around, new tests are done. But, in the mean time, reasonable people will go with what the science says, not what old adages claim baselessly. If your adage has any REAL base, I've yet to see the study.

I am afraid you'd start twisting them as you did with my other numerical examples

Lich Mong wrote:

I would hope you would understand

Lich Mong wrote:

in an attempt to "prove me wrong,"

Lich Mong wrote:

The very fact I have to explain

Lich Mong wrote:

you either are very stupid

Lich Mong wrote:

you're trying to misrepresent me to "save face" or whatever

Lich Mong wrote:

please don't think I don't know what you're doing.

Lich Mong wrote:

I think you need to look up the definition of "under."

Lich Mong wrote:

you had blinders on at this point

Lich Mong wrote:

going after each of my statements individually instead of in context

Lich Mong wrote:

it was a very very stupid thing to say

Lich Mong wrote:

just how little you understand statistics and polls.

Lich Mong wrote:

I thought when you referred to my standard deviation link as "condescending" it meant you had at least a rudimentary understanding

Lich Mong wrote:

it became clear to me just how little you know.

Lich Mong wrote:

you do not even really understand the subject anyway

Lich Mong wrote:

don't grasp the process that goes into numbers like those

Lich Mong wrote:

feel this is a "who's wrong/right how can I showoff" discussion

Lich Mong wrote:

try to make me look as foolish as you can

Lich Mong wrote:

I'll not respond (hopefully, if I pass my willsave this time).

Lich Mong wrote:

So, chalk it up as a "win" if you want.

All of this is exactly the very sort of phony argumentation that you accusing me of employing. All of this is trying to make me look foolish without actually debating or employing reasoning, exactly as you accusing me of doing. All of this is you trying to "win" the conversation, which is exactly what you end up accusing me of doing. All of this is pure bullshit. I don't think I have ever come across a more hypocritical post here at Sinfest. I think you're pretty pathetic._________________"To love deeply in one direction makes us more loving in all others."
- Anne-Sophie Swetchine

Yes, I did. You would have to show that comparing the in numbers to the out numbers across fields were comparable before you could compare them as you did. Each field could(and likely does) have drastically different drop out rates, so the in and out numbers for each has a different variation, since they change at different rates.

I agree with you that each field would have it's own drop out rate, and that each drop out rate would have a different variation. Nonetheless I do not "have to" measure how comparable the fields are, because it is still meaningful that proportionally more women finish Engineering than do men, and it is also still meaningful that Engineering is the field in which that is most true, against the trend the other fields show.

Lich Mong wrote:

If more Engineers drop out than other fields then the change in gender for Engineers would be expected to be more drastic, even if the gender of the people dropping out was perfectly random.

Of course. And having that extra information would let us draw measured and more precise conclusions from the data. We could even mathematically express our confidence in our conclusions! Nonetheless, even without that extra information, we can still draw some conclusions from the data, and those conclusions can still be valid.

Lich Mong wrote:

Or you don't realize I was referring to the intake numbers, not the outtake ones.

You are rather overdramatising my misreading. You switched from talking about over regarding the bet, to under, regarding the number. I can't help but notice you were uninterested in engaging with the point I made, though. Allow me to rephrase: "The number could be 23% or 22% or 21%, and my statements would all still be perfectly reasonable."

You are unmistakably wrong about a 1% change having an effect on the validity of my conclusions. If you don't want to admit it, that's fine, but please don't pretend you've answered me when you didn't even try to do so.

Lich Mong wrote:

However, when you started talking about how you assumed the numbers might came from every school everywhere and that you could not see how it would matter as long as the numbers were "representative" it became clear to me just how little you know. You clicking that 'condescending' link might have prevented this whole stupid argument. Now, this is not to call YOU stupid or something, but is to say I don't feel it would be instructive for either of us for me to have to fight through your strawmen and shifting goal posts if you do not even really understand the subject anyway.

If the data is taken directly from complete data, my conclusion is valid. If the data is based on as much data as they could gather, whether it is a quarter or a half of the total data, my conclusion is valid. If the data is based on a representative sample of students, my conclusion is valid.

You did not answer what I'm saying here. You didn't tell me why I'm wrong. You just told me that I'm so stupid you're not going to bother answering, even though, no doubt, you could do so easily and definitively, because as you've made abundantly clear, you've studied this formally. Every time some wanker has used this tactic on me in any conversation I've ever been it, it's been because they were completely full of shit. I can't help but conclude that you are full of shit as well.

Lich Mong wrote:

So, chalk it up as a "win" if you want.

Awesome. I keep a slate right next to the computer to keep track of such things. Thanks for making this one easy - sometimes I accidentally have mutually informative conversations, which are very hard to score.

The few arguments you have bothered to make, other than the pure posturing ones, boil down to needing more information for the data to be useful. That is wrong. More information would certainly make the information more useful, but it is perfectly reasonable to draw conclusions, even when you don't have as much data as you would like._________________"To love deeply in one direction makes us more loving in all others."
- Anne-Sophie Swetchine

Looks like I failed that save (not surprising really, I have a low wisdom modifier).
Anyway, if you look between those pieces you will see not only reasoning, but links to specific examples.

However, it's true when you cut up my post to remove both its content and its context it becomes devoid of reasoning. Not even I can argue with that simple fact.

And now we are having an argument about the argument. Neither your last post nor this one here I'm writing contain anything about the original issue (my last one did, but now it lies in shattered pieces at our feet) . I can only assume that was your plan all along.

However, it's true when you cut up my post to remove both its content and its context it becomes devoid of reasoning.

Please do tell me where you answered my contention that a 1% shift in intake wouldn't be nearly large enough to invalidate my conclusion. And please repeat your answer about why the sample size would make my conclusion invalid. I genuinely cannot find these things in any of your posts.

Lich Mong wrote:

Neither your last post nor this one here I'm writing contain anything about the original issue

My Last Post wrote:

I agree with you that each field would have it's own drop out rate, and that each drop out rate would have a different variation. Nonetheless I do not "have to" measure how comparable the fields are, because it is still meaningful that proportionally more women finish Engineering than do men, and it is also still meaningful that Engineering is the field in which that is most true, against the trend the other fields show.

Whoops. Looks like actually I reiterated pretty much the entirety of the original issue. Doesn't seem to support your position that I am the one trying to change the subject._________________"To love deeply in one direction makes us more loving in all others."
- Anne-Sophie Swetchine

Here I will use another hypothetical numerical example to explain, which you can claim is my whole argument and take out of context to use against me, again.

Lets say 100 students are polled, 50% boys and 50% girls, in two different fields, field A and field B. In field A that year 10 people polled drop out, 7 boys and 3 girls. So, 48% are boys and 52% are girls, and 70% of the dropouts are boys.

Now, in field B 85 people drop out, 45 guys and 40 girls, so the dropout % is 52% guys, but the new passing rate is 67% girls.

However, those 100 polled students are from a larger population of ~1000 students. Assuming a simple binomial distribution, that means our original poll numbers had a +3(student) standard error. (But, assuming an uniform distribution, for real hypothesis testing you would want to be within the 95% confidence interval, so you're really looking at ~+6) So, none of these numbers have a statistically significant difference in gender.

However, again, this is all a waste in your case anyway, because we don't know what the change in the rate is year to year is for the gender by field._________________A MtG Webcomic

So, none of these numbers have a statistically significant difference in gender.

Sure. These numbers are not statistically significant enough to meet the 95% confidence interval standard you've set. Further, I accept that your 95% confidence interval is a good minimum standard for responsible use of statistics (for managerial decisions or policymaking or whatever decisions might use numbers like these).

First point: You do not need to be statistically significant enough to be within a 95% confidence interval standard to claim that data implies something. I have said the data in question imply that Ember is wrong. They do. They would, even if they weren't statistically significant enough to meet your standard.

Now, please answer a question for me. Do you think there is any chance in hell that the numbers you've posted from the Council of Graduate Schools are anywhere near as flimsy as your example numbers?

Second point: I guarantee you that they are not. Seriously, expand your fields to 10, and your poll size to 1000 from each field (much less than 10% of the total, I would think). You will find that your numbers are no longer statistically insignificant.

I don't have any idea what the Council of Graduate schools is, but they sound official enough and educated enough that I don't think they'd be publishing if they'd polled 200 people. That your criticism could be worthwhile in the case of outrageously shallow numbers does not make it worthwhile about numbers whose robustness we have no reason to doubt.

Third point: If I was completely wrong, my trust in the Council demonstrated unwise, if I was tricked by their canny use of tenths of a percent, if I have built my house upon the sand, then the numbers would still imply that Ember was wrong. The problem would lie in the methodology that achieved the numbers, not in my use of the numbers.

Lich Mong wrote:

However, again, this is all a waste in your case anyway, because we don't know what the change in the rate is year to year is for the gender by field.

The first time you said this, I agreed that the change from year to year would make the conclusions we could draw more accurate and measurable. I have said so in pretty much every post thus far. I have also added, in pretty much every post thus far, that the numbers are good enough to imply things, even without that data added. You never answer me. I don't know how to continue on this point if you don't acknowledge that I am saying something.

Finally, please imagine the data are there. Imagine your response to several years worth of data, data which is pretty similar to the 2010 numbers. What would you conclude?

Now simply apply that you agree that those numbers are probably correct. That means that the conclusion you had in mind is probably correct! When I say that the numbers imply that Ember is wrong, it is based on exactly the same things that went on in your head when you agreed that the last five years data probably had numbers around the same mark._________________"To love deeply in one direction makes us more loving in all others."
- Anne-Sophie Swetchine

I mean shit you guys are never going to agree. Why continue? It is purposeless.

And it's really as easy as just not replying to whatever the disagreement was. Some people called me wrong and unintelligent and shit like that, but I didn't reply and guess what the world didn't end. (although this might spark it back up again, but I'll just ignore that and then the conversation will end for real).

You don't have to force someone to change their opinions. Doing so in my opinion is just plain rude.

I seriously don't understand this compelling need to prove others wrong or get them to change their minds. It's like oh you have opinions, well fuck those you're now going to change your opinion to whatever I believe because I'm the most important little shit on the planet and it's very important that you and I have the same beliefs. If we don't I'm just going to get really angry and ruin any chances of a positive relationship with you at all.

Sure. These numbers are not statistically significant enough to meet the 95% confidence interval standard you've set. Further, I accept that your 95% confidence interval is a good minimum standard for responsible use of statistics (for managerial decisions or policymaking or whatever decisions might use numbers like these).

It's not "my minimum standard" is the one used by most fields for hypothesis testing.

Sojobo wrote:

First point: You do not need to be statistically significant enough to be within a 95% confidence interval standard to claim that data implies something. I have said the data in question imply that Ember is wrong. They do. They would, even if they weren't statistically significant enough to meet your standard.

You're allowed to say whatever you want.

The question is if you want it to be meaningful or not.

Sojobo wrote:

Now, please answer a question for me. Do you think there is any chance in hell that the numbers you've posted from the Council of Graduate Schools are anywhere near as flimsy as your example numbers?

My numbers has a statistical power of .1, which is much much better than most political polls you see, for example. I would suspect they used a smaller % of the student population.

However, if they had larger numbers then they might have a smaller errors, depending on overall size. But, IDK what they had. They did not print errors and it's clearly not mean to be a scientific poll.

Sojobo wrote:

Second point: I guarantee you that they are not. Seriously, expand your fields to 10, and your poll size to 1000 from each field (much less than 10% of the total, I would think). You will find that your numbers are no longer statistically insignificant.

The number of fields is immaterial since each one is treated differently. For 1000 people each one would have a different error for each field based on the overall size of the feild.

For your 1000 people example, I did a quick back-of-the-envelope calculation(which i still have even though my browser ate my post, thank God) and came up with a 35 student error for US graduate engineers, so....

I guess this is the part you throw other numbers it might have been at me until I give you an error you like? I mean, it might have been 2000 or 127 or 13050; those are all numbers. Why don't you pick one until I tell you the error is 1% and you can claim that was the number you suspected all along.

Sojobo wrote:

I don't have any idea what the Council of Graduate schools is, but they sound official enough and educated enough that I don't think they'd be publishing if they'd polled 200 people. That your criticism could be worthwhile in the case of outrageously shallow numbers does not make it worthwhile about numbers whose robustness we have no reason to doubt.

It depends on what they were trying to show. The poll was not scientific or they would have given errors.
Also, they clearly were not trying to show what you were trying to show or they would have simply polled dropout numbers.

Sojobo wrote:

Third point: If I was completely wrong, my trust in the Council demonstrated unwise, if I was tricked by their canny use of tenths of a percent, if I have built my house upon the sand, then the numbers would still imply that Ember was wrong. The problem would lie in the methodology that achieved the numbers, not in my use of the numbers.

Their methodology could still be right(and likely is) because they were not trying to show what you're trying to show.

Your methodology is wrong because you are trying to compare things that aren't comparable. The 2010 admission %'s are not comparable to the 2010 graduation %'s. You are comparing apples and oranges. You can't infer what you trying to infer from that poll. Which makes me ask again why you don't go find the numbers you DO need.

I feel like I'm the only one doing research for this.

Sojobo wrote:

I have also added, in pretty much every post thus far, that the numbers are good enough to imply things, even without that data added. You never answer me.

I. have. in. every. post.
You can't infer what you want to infer from those numbers. I don't know how many more times I have to say it, how many more examples I have to give, or how much more research and numbers I have to crunch to get through to you.
Those. numbers. do. not. imply. what. you. want. them. to. imply.

You don't have to force someone to change their opinions. Doing so in my opinion is just plain rude.

If you feel that you probably shouldn't have come to the internet asking for proof of the converse.

I think it's rude to ask for something and then get mad when someone gives it to you.

Also, some opinions are wrong. Most people used to be of the opinion the Sun revolved around the Earth, for example. Turns out --and you'd never guess this just standing in your backyard--it does not._________________A MtG Webcomic

You don't have to force someone to change their opinions. Doing so in my opinion is just plain rude.

If you feel that you probably shouldn't have come to the internet asking for proof of the converse.

I think it's rude to ask for something and then get mad when someone gives it to you.

Also, some opinions are wrong. Most people used to be of the opinion the Sun revolved around the Earth, for example. Turns out --and you'd never guess this just standing in your backyard--it does not.

Well anyone who looks up at the stars can see they change and deduce that we have to be moving. Not that hard a deduction.

And when have I ever asked for something?

And even then why does it matter if their opinion is wrong. So someone believes the world is flat. Who the fuck cares. Why is it so important that he believe the world is spherical? People believed the world was flat for thousands of years and it didn't really kill them.

Besides the arguing never changes anyone's mind anyway. You just go on and on and it becomes stupid.

And with that I'll end my opinion since I could give a shit what you think anyway. If you want to go on wasting your time with pointless arguments go ahead. I'll continue to just post my opinions and reasoning and I'll have fun with that while you argue and I guess you can have fun with that.

And so, our heroes reached Page Twenty-Three. They had faced many hardships, but they had finally decided to put their differences behind them and stop talking about things. Their situation might have been looking up, but little did they realize that the long, heated debate about internet debates was nigh upon them. HUAHAHAHAHAHAAAAA_________________butts

Well anyone who looks up at the stars can see they change and deduce that we have to be moving. Not that hard a deduction.

Yes, actually it is. That's why it took professionals to figure it out. Also, the Sun moves differently in the sky than the stars; it was the motion of the planets that was first used. The motion of the stars was used to refute the idea of a heliocentric universe.

Also--and I think this is my real point--you'd actually have to go out and LOOK and research that information; against what you're senses were telling you about the Earth not appearing to move. Just looking up at the sky every now and again and making inferences would get you the wrong answer.

Ember778 wrote:

And when have I ever asked for something?

You asked for a psychologist to explain it better, when they did you told them what they did was "not science." You asked for empirical evidence, when you got it you asked for a double blind study explicitly.

Ember778 wrote:

And even then why does it matter if their opinion is wrong. So someone believes the world is flat. Who the fuck cares.

I do.
You mean to tell me if someone you new told you they thought the Earth was flat you'd be "That's cool man, I have opinions too" about it?

You've NEVER told anyone their opinion was wrong, or never wanted to?

Ember778 wrote:

Besides the arguing never changes anyone's mind anyway. You just go on and on and it becomes stupid.

Speaking from personal experience, this is untrue. My opinions have change quite a bit over the years.
I find convincing arguments to be convincing. I also find arguments back by logic and evidence can change my mind, especially if I see I have less of both.
But, that might just be me.

Ember778 wrote:

And with that I'll end my opinion since I could give a shit what you think anyway. If you want to go on wasting your time with pointless arguments go ahead. I'll continue to just post my opinions and reasoning and I'll have fun with that while you argue and I guess you can have fun with that.

If you don't give a shit what I think about what you think you might want to stop telling me what you think. I tend to think about things I'm told about.
But -again- that might just be me._________________A MtG Webcomic